Digital Logic design Help PLZ

Hi everybody ..
I need UR Help ASAP plz .
Im taking digital logic design course & I have some problems to be solved
SO If Anybody could help me I would be thankful
Here R the problems

1) A combinational Logic Circuit has 4 inputs ( A,B,C & D ) and One output Z . The output is iff the input has three consecutive Zeros or three consecutive ones . For example , If A=1, B=0 , c=0 and D=0 then Z=1 , but if A=0 , B=1 , C=0 and D=0 then Z=0
Design the circuit using one 4-input OR gate and 4 3-input AND gates .

2) Design a combinational logic circuit which has one output Z and a 4-bit input ABCD representing a binary number Z . Z should be 1 iff the input is at least 5 , but is no greater than 11 . Use one OR gate ( three inputs ) and three AND gates ( with no more than three inputs each ) .

3) A bank vault has three locks with a different key for each lock . Each Key is owned by a differefnt person . In order to open the door , at least two people must insert their keys into the assigned locks . The signal lines A,B,C are 1 if ther is a key inserted into lock 1,,2 or 3 respectively . write an equation for the variable Z which is 1 iff the door should open .

It is probably a trick question (at least #1). There is no way to know the four states without being able to test by inversion. You can't do much with positive logic alone, but you can do anything with inverting logic.

If your instructor insists that it is possible with the 4 AND gates and the one OR, please post it up. I'd like to see it.

Hi everybody ..
I need UR Help ASAP plz .
Im taking digital logic design course & I have some problems to be solved
SO If Anybody could help me I would be thankful
Here R the problems

1) A combinational Logic Circuit has 4 inputs ( A,B,C & D ) and One output Z . The output is iff the input has three consecutive Zeros or three consecutive ones . For example , If A=1, B=0 , c=0 and D=0 then Z=1 , but if A=0 , B=1 , C=0 and D=0 then Z=0
Design the circuit using one 4-input OR gate and 4 3-input AND gates .

2) Design a combinational logic circuit which has one output Z and a 4-bit input ABCD representing a binary number Z . Z should be 1 iff the input is at least 5 , but is no greater than 11 . Use one OR gate ( three inputs ) and three AND gates ( with no more than three inputs each ) .

3) A bank vault has three locks with a different key for each lock . Each Key is owned by a differefnt person . In order to open the door , at least two people must insert their keys into the assigned locks . The signal lines A,B,C are 1 if ther is a key inserted into lock 1,,2 or 3 respectively . write an equation for the variable Z which is 1 iff the door should open .